MinT - Best Known (60−35, 60, s)-Nets in Base 81

Best Known (60−35, 60, s)-Nets in Base 81

(60−35, 60, 370)-Net over F₈₁ — Constructive and digital

Digital (25, 60, 370)-net over F₈₁, using

t-expansion [i] based on digital (16, 60, 370)-net over F₈₁, using
- net from sequence [i] based on digital (16, 369)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370, using
    - a function field by GarcÃa and Quoos [i]

(60−35, 60, 411)-Net over F₈₁ — Digital

Digital (25, 60, 411)-net over F₈₁, using

Gilbertâ€“VarÅ¡amov bound [i]

(60−35, 60, 377060)-Net in Base 81 — Upper bound on s

There is no (25, 60, 377061)-net in base 81, because

1 times m-reduction [i] would yield (25, 59, 377061)-net in base 81, but
- the generalized Rao bound for nets shows that 81^mÂ â‰¥ 39867 547467 207894 517016 080095 764814 939589 504548 533531 553289 839791 339636 769894 471809 895884 802854 926080 973335 689361 > 81⁵⁹ [i]